Beyond the constant Lorenz number for separating thermal conductivities of electrons and phonons: A DFT study

Lorenz number is an important quantity for separating thermal conductivities of electrons and phonons in the field of thermoelectrics, which is material- and temperature-dependent. Combing DFT calculations with Boltzmann transport equations, we have derived the Lorenz number for realistic compound BaAu$_6$Ge$_{40}$, a good thermoelectric material. It is demonstrated that using the constant Lorenz number of the Wiedemann-Franz law for simple metals leads to strong discrepancies, in particular at higher temperatures. The results suggest that one has to rethink the way of extracting both $\kappa_{el}$ and $\kappa_{ph}$ as usually done based on the measured electrical conductivity. We propose a strategy of correcting the Wiedemann-Franz Lorenz number that subtracts the metallic limiting value by S$^2$ as obtained from Seebeck measurements.